Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 20, Problem 22PQ
To determine
Plot the letters versus frequency of the ball landing in a particular square and to find the letter which is most probable occurrence.
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The Earth's atmosphere is composed of about 78 percent nitrogen, 21 percent
oxygen, 0.9 percent argon, and 0.1 percent other gasses. To find out why these
gasses are "trapped" in the earth's atmosphere, consider a projectile with mass m
that is about to launch vertically upward from earth.
a. Ignore air resistance, show that the projectile can only escape the magnetic
pull of the earth if it is launched vertically upward with a kinetic energy greater
than mgRearth, where g = 9.80 m/s? and the earth's radius Rearde = 6378 km.
b. Compute the temperature required by a nitrogen molecule (molar mass 28.0
g/mol) and an oxygen molecule (molar mass 32 g/mol) to achieve the average
translational kinetic energy required to escape earth?
c. Repeat part (b) for the moon, for which g = 1.63 m/s? and Rmoon = 1740 km.
d. Present your conclusion on the atmosphere of earth and moon based on the
results from parts (b) and (c).
Question B2
Consider a one-dimensional chain of atoms, each joined to its nearest neighbours by a bond
of spring constant J. The unit cell, of length a, contains one large atom of mass M, which
we label = 1, and two smaller atoms of mass m, which we label l = 2 and l = 3. We
denote the displacement of the eth atom in the nth unit cell by ur (note that this does not mean
exponentiation):
n-1
u
+1
mm mmmmm M
m
m
M
m m
a
a) Give an expression for the force on each atom, F1, F2 and F3, in terms of the atomic
displacements u.
b) Use the standard ansatz
u = u exp (i(kna - wt))
to write the equations of motion for this chain in the form
(1)
01
=
Pū²
03
0
where P is a 3 x 3 matrix. (Do not attempt to diagonalise this matrix.)
(2)
c) Show that at the Brillouin zone boundary (k = π/a), one solution to your matrix equation (2)
is u₁ = 0, u² = u³ = 1.
Calculate the angular frequency w of this mode.
Explain why this value is independent of M.
Is your answer consistent with the solution for a…
Most of the mass of an atom is in its nucleus. Model the mass distribution in a diatomic molecule as two spheres of uniform density, each of radius 2.00 x 10-15 m and mass 1.00 x 10-26 kg, located at points along the y axis as in 42.5a, and separated by 2.00 x 10-10 m. Rotation about the axis joining the nuclei in the diatomic molecule is ordinarily ignored because the first excited state would have an energy that is too high to access. To see why, calculate the ratio of the energy of the first excited state for rotation about the y axis to the energy of the first excited state for rotation about the x axis.
Chapter 20 Solutions
Physics for Scientists and Engineers: Foundations and Connections
Ch. 20.2 - In Example 20.1, we found that the rms value of a...Ch. 20.3 - If the temperature of a gas is doubled, what...Ch. 20.3 - Prob. 20.3CECh. 20.5 - Prob. 20.4CECh. 20.7 - Prob. 20.5CECh. 20.8 - Prob. 20.6CECh. 20 - Prob. 1PQCh. 20 - Prob. 2PQCh. 20 - Prob. 3PQCh. 20 - Prob. 4PQ
Ch. 20 - Prob. 5PQCh. 20 - Prob. 6PQCh. 20 - Prob. 7PQCh. 20 - Prob. 8PQCh. 20 - Particles in an ideal gas of molecular oxygen (O2)...Ch. 20 - Prob. 10PQCh. 20 - Prob. 11PQCh. 20 - Prob. 12PQCh. 20 - Prob. 13PQCh. 20 - Prob. 14PQCh. 20 - The mass of a single hydrogen molecule is...Ch. 20 - Prob. 16PQCh. 20 - The noble gases neon (atomic mass 20.1797 u) and...Ch. 20 - Prob. 18PQCh. 20 - Prob. 19PQCh. 20 - Prob. 20PQCh. 20 - Prob. 22PQCh. 20 - Prob. 23PQCh. 20 - Prob. 24PQCh. 20 - Prob. 25PQCh. 20 - Prob. 26PQCh. 20 - Prob. 27PQCh. 20 - Prob. 28PQCh. 20 - Consider the Maxwell-Boltzmann distribution...Ch. 20 - Prob. 30PQCh. 20 - Prob. 31PQCh. 20 - Prob. 32PQCh. 20 - Prob. 33PQCh. 20 - Prob. 34PQCh. 20 - Prob. 35PQCh. 20 - Prob. 36PQCh. 20 - Prob. 37PQCh. 20 - Prob. 38PQCh. 20 - Prob. 39PQCh. 20 - Prob. 40PQCh. 20 - Prob. 41PQCh. 20 - Prob. 42PQCh. 20 - Prob. 43PQCh. 20 - Prob. 44PQCh. 20 - Figure P20.45 shows a phase diagram of carbon...Ch. 20 - Prob. 46PQCh. 20 - Prob. 47PQCh. 20 - Consider water at 0C and initially at some...Ch. 20 - Prob. 49PQCh. 20 - Prob. 50PQCh. 20 - Prob. 51PQCh. 20 - Prob. 52PQCh. 20 - Prob. 53PQCh. 20 - Prob. 54PQCh. 20 - Prob. 55PQCh. 20 - Prob. 56PQCh. 20 - Consider again the box and particles with the...Ch. 20 - Prob. 58PQCh. 20 - The average kinetic energy of an argon atom in a...Ch. 20 - For the exam scores given in Table P20.60, find...Ch. 20 - Prob. 61PQCh. 20 - Prob. 62PQCh. 20 - Prob. 63PQCh. 20 - Prob. 64PQCh. 20 - Prob. 65PQCh. 20 - Prob. 66PQCh. 20 - Determine the rms speed of an atom in a helium...Ch. 20 - Consider a gas filling two connected chambers that...Ch. 20 - Prob. 69PQCh. 20 - Prob. 70PQCh. 20 - A 0.500-m3 container holding 3.00 mol of ozone...Ch. 20 - Prob. 72PQCh. 20 - Prob. 73PQ
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